Hausdroff Graphs

A simple graph G is said to be Hausdorff if for any two distinct vertices u and v of G, one of the following conditions hold:
1. Both u and v are isolated
2. Either u or v is isolated
3. There exist two non-adjacent edges e1 and e2 of G such that e1 is incident with u and e2 is incident with v:
In this paper we discuss Hausdorff graphs and some examples of it. This paper also deals with the sucient conditions for Kmn, join of two graphs, middle graph of a graph and corona of two graphs to be Hausdorff. The line graph of a given Hausdorff graph is Hausdorff is proved. Moreover, the relations between Hausdorff graph with its incidence matrix and its adjacency matrix are discussed.